Abstract
Recently Lutz [14,15] introduced a polynomial time bounded version of Lebesgue measure. He and others (see e.g. [11,13,14,15,16,17,18,20]) used this concept to investigate the quantitative structure of Exponential Time (E=DTIME(2lin)). Previously, Ambos-Spies, Fleischhack and Huwig [2,3] introduced polynomial time bounded genericity concepts and used them for the investigation of structural properties of NP (under appropriate assumptions) and E. Here we relate these concepts to each other. We show that, for any c≥1 the class of nc-generic sets has p-measure 1. This allows us to simplify and extend certain p-measure 1-results. To illustrate the power of generic sets we take the Small Span Theorem of Juedes and Lutz [11] as an example and prove a generalization for bounded query reductions.
The first author was supported in part by the Human Capital and Mobility program of the European Community under grant CHRX-CT93-0415; the third author was supported by the Dutch VSB foundation during the time of this research.
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© 1994 Springer-Verlag Berlin Heidelberg
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Ambos-Spies, K., Neis, HC., Terwijn, S.A. (1994). Genericity and measure for exponential time. In: Prívara, I., Rovan, B., Ruzička, P. (eds) Mathematical Foundations of Computer Science 1994. MFCS 1994. Lecture Notes in Computer Science, vol 841. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58338-6_69
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DOI: https://doi.org/10.1007/3-540-58338-6_69
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